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#1 2009-06-29 02:45:46

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Understanding Ratio to Scale ?

How to calculate the ratio to scale for anything. Example you have a object that is a

scale what does this mean? And how do you figure out scale?

Last edited by SuperLynx (2009-06-29 02:46:33)

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#2 2009-06-29 04:23:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: Understanding Ratio to Scale ?

Hi SuperLynx;

This will give you the background.
http://en.wikipedia.org/wiki/Scale_model

Its for scaling objects down to smaller size but keeping all the relevant ratios the same as in making a scale model. For instance 1:48  could mean 1/4 of an inch represents a foot. 1 : 15 could mean 1 foot represesnts 15 ft. You have to be told the units of measure.  On a map you will see a scaling like 1 inch represents 1 mile. The scaling here is 1:63360


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2009-06-30 02:41:11

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

How do you figure it out ?

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#4 2009-06-30 07:29:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: Understanding Ratio to Scale ?

Hi SuperLynx;

  The scaling is given to you on the map or the model. Say you are told that 1 inch represents 1 mile on the map, the scaling is figured like this.

12 (inches per foot) * 5280 (feet in a mile) = 1:63360 because there are 63360 inches in a mile.

  Suppose you had a model boat and are told that the model is 1/10 actual size this means the scaling is 1:10. So if that model was 3 ft long that means the actual boat is 30 ft long.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2009-06-30 23:46:53

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

Can you reverse something ? As in say I found out a model car is 1:25 in scale how can I find out the size of that ?

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#6 2009-06-30 23:54:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: Understanding Ratio to Scale ?

Hi SuperLynx;

The real car is 25 times the size of the model. It is as if you you put the model under a microscope that magnified it 25 times.

Last edited by bobbym (2009-06-30 23:55:19)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2009-07-01 00:58:51

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

If I said to you my car model is 1:25 could you tell me the actual size from a 1:25 scale ?

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#8 2009-07-01 06:36:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: Understanding Ratio to Scale ?

Hi SuperLynx;

Sure, measure the length of the model and now multiply by 25. Then measure the width and height and multiply each by 25.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2009-07-01 09:03:18

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

So if that model was 3 ft long that means the actual boat is 30 ft long.

- How do you figure this out ? I'm a little confused by that sentence.

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#10 2009-07-01 17:13:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: Understanding Ratio to Scale ?

Hi SuperLynx;

If the model were 3 feet long and it was 1:25, the actual size of the boat is 25 *3 or 75 ft long. 1:25 is a proportion it is saying that the model is 1/25 the size of the boat. If you have ever seen in a book a picture that said 1/3 actual size, this meant a scaling of 1:3. The actual object is 3 times the size of that picture.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2009-07-02 03:03:39

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

I think I understand now, but I'm going to put it into practice and if I shall have any problems I'll just ask smile

Thank You.

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#12 2009-07-02 17:55:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: Understanding Ratio to Scale ?

Hi SuperLynx;

  Glad you are understanding.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2013-04-05 04:34:21

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

I have to re-surface this old thread. 
Suppose I have a book, that was designed at 27 inches across / 24 inches tall / 7 inches think.  Obviously a book for a giant, not for a human to read.  How I calculate the ratio so the book is; 7 inches across / 9 inches tall / inch thick ?

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#14 2013-04-05 19:51:03

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,269

Re: Understanding Ratio to Scale ?

hi SuperLynx

27:24:7 cannot become 7:9:?  because there is no consistent ratio here.

To reduce from 27 to 7 you need a multiplier of x(7/27)

Apply that to 24 and you will get 24 x 7 /27 = 8 x 7 / 9 = 56/9 = 6.2222

You will have to choose one pair to get the multiplier from that and then apply it to both the other numbers.

eg 7 x 7/27 = 1.82 would then be the third measurement giving 7 : 6.2 : 1.8

or using 24 --> 9 makes a multiplier of x 9 / 24 and the ratios are then (27 x 9/24) : 9 : 7 x 9/24

In general the multiplier is x (new value) / (old value)

Hope that helps,  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2013-04-07 06:35:08

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

Where did you get the multiplier of X ?

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#16 2013-04-07 10:19:43

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,269

Re: Understanding Ratio to Scale ?

That x is just a times sign.

Put the new value over the old and that's the fraction to multiply by.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#17 2013-04-13 16:10:58

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

bob bundy wrote:

hi SuperLynx

27:24:7 cannot become 7:9:?  because there is no consistent ratio here.

To reduce from 27 to 7 you need a multiplier of x(7/27)

Apply that to 24 and you will get 24 x 7 /27 = 8 x 7 / 9 = 56/9 = 6.2222

You will have to choose one pair to get the multiplier from that and then apply it to both the other numbers.

eg 7 x 7/27 = 1.82 would then be the third measurement giving 7 : 6.2 : 1.8

or using 24 --> 9 makes a multiplier of x 9 / 24 and the ratios are then (27 x 9/24) : 9 : 7 x 9/24

In general the multiplier is x (new value) / (old value)

Hope that helps,  smile

Bob

I need to divide 7/27 then apply that to 24 ? I'm not following smile

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#18 2013-04-13 19:46:07

SteveB
Member
Registered: 2013-03-07
Posts: 555

Re: Understanding Ratio to Scale ?

When you are converting a ratio by scaling it up or down you have to multiply or divide the components by the same number.

It is not possible to put the ratio  27 : 24 : 7  into the form  7 : 9 : ?

This can be proven by first calculating the number you would have to use to multiply 27 by something to get to 7 and then
testing whether the same number can be multiplied by 24 to get 9

The number (7/27) = 0.259259...... (recurring decimal) can be multiplied by 27 to get 7

but if we multiply this by 24 it results in 6.2222222  (but 9 was needed)

I did wonder whether the 7 and the 9 were the wrong way round. This does not work either, but is closer.

(27 divided by 3 gets 9 but 24 divided by 3 gives us 8 rather than 7)

If you consider the 7 bit to be right but do not know the other two numbers then you can do the scaling down but you
get something like this:  7 :  6.222222...  :  1.8148148....

Or if it were 9 as the initial number you might get:  9 : 8 : 2.3333....
or if the second component of the second ratio 9 were correct we get:  10.125 : 9 : 2.625
(That assumes that the ratio 27 : 24 : 7 is correct )

Last edited by SteveB (2013-04-13 19:51:41)

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#19 2013-04-13 20:10:07

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,269

Re: Understanding Ratio to Scale ?

hi SuperLynx

if you want to maintain a ratio whilst re-scaling the numbers you need to work out a multiplier that will do this.

Let's say we use the 27 becomes 7 values to work out the multiplier.  The way to get a multipler is like this:

So that would make the multipler:

Let's check it works:

Now use the same multiplier to get the other two values in the ratio.

That's the problem. 

A similar problem arises if you try to use 24 and 9 to get a multiplier.

Are you sure that the original problem is typed correctly?

Bob

View Image: SuperLynx.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#20 2013-04-14 00:44:03

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

SteveB wrote:

When you are converting a ratio by scaling it up or down you have to multiply or divide the components by the same number.

It is not possible to put the ratio  27 : 24 : 7  into the form  7 : 9 : ?

This can be proven by first calculating the number you would have to use to multiply 27 by something to get to 7 and then
testing whether the same number can be multiplied by 24 to get 9

The number (7/27) = 0.259259...... (recurring decimal) can be multiplied by 27 to get 7

but if we multiply this by 24 it results in 6.2222222  (but 9 was needed)

I did wonder whether the 7 and the 9 were the wrong way round. This does not work either, but is closer.

(27 divided by 3 gets 9 but 24 divided by 3 gives us 8 rather than 7)

If you consider the 7 bit to be right but do not know the other two numbers then you can do the scaling down but you
get something like this:  7 :  6.222222...  :  1.8148148....

Or if it were 9 as the initial number you might get:  9 : 8 : 2.3333....
or if the second component of the second ratio 9 were correct we get:  10.125 : 9 : 2.625
(That assumes that the ratio 27 : 24 : 7 is correct )

I have to always divide the smallest number of a larger ratio into the bigger number ? If so I'm always going to get a decimal.

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#21 2013-04-14 05:18:12

SteveB
Member
Registered: 2013-03-07
Posts: 555

Re: Understanding Ratio to Scale ?

I have to always divide the smallest number of a larger ratio into the bigger number ? If so I'm always going to get a decimal.

Firstly it does not really matter if you get a decimal and second you do not necessarily have to be concerned about whether the
number/ratio you are trying to transform is smaller or larger.

On the other hand whole numbers are nice to work with and it may be easier to try to get a result which only has whole numbered
components. In this case you are scaling the thing down as I understand it so there is perhaps a greater chance of ending up with
a number which requires digits after the decimal point. (It is a fact of life that numbers requiring a decimal point are more common.)

Here is an example of a ratio conversion that converts a higher set of numbers to a lower set with whole numbers only:

3 : 6 : 9   is the same as  1 : 2 : 3  (here I have divided each element of the ratio by 3 I could have multiplied by one third)

(obviously that example does not have the same ratio as your problem)

If the second ratio contained only two elements and I wanted to find the third then it can only be done if the two I have given are
in the correct ratio. If I chose 4 : 7 : ? then that would not be possible for 3 : 6 : 9 however if I change the 7 to an 8 then we get
4 : 8 : 12

In your example in the earlier post the problem is that the two numbers you gave for the new ratio are already incorrect relative
to each other. In other words one must be changed. Either the original measurements are wrong or the two numbers in the
second ratio are not in the right ratio relative to each other. The fact that the second number is larger than the first, but the other
way round in the other ratio immediately alerts a mathematician to an inconsistent proportion.

If I have the ratio 3 : 6 : 9 and I want a model to be 1 : 7 : ???  then the first number has to go from 3 to 1, but the second has
to go from 6 to 7, with the same multiplication. Well this is not going to work because 3 multiplied by a third equals 1
but if I do the same multiplication to the second number 6 get transformed to 2. One cannot go up and the other down.
In fact the two numbers that we give for the second ratio have to be in the correct ratio of the first two numbers of the first ratio.
It would probably by a good idea to look at Bob's post including the image file he posted (if you haven't already done so).
Trying to explain this using plain text only is not easy and could cause confusion.

Anyway I hope that has cleared the matter up rather than muddied the waters even further.

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#22 2013-04-19 17:41:30

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

SteveB wrote:

I have to always divide the smallest number of a larger ratio into the bigger number ? If so I'm always going to get a decimal.

Firstly it does not really matter if you get a decimal and second you do not necessarily have to be concerned about whether the
number/ratio you are trying to transform is smaller or larger.

On the other hand whole numbers are nice to work with and it may be easier to try to get a result which only has whole numbered
components. In this case you are scaling the thing down as I understand it so there is perhaps a greater chance of ending up with
a number which requires digits after the decimal point. (It is a fact of life that numbers requiring a decimal point are more common.)

Here is an example of a ratio conversion that converts a higher set of numbers to a lower set with whole numbers only:

3 : 6 : 9   is the same as  1 : 2 : 3  (here I have divided each element of the ratio by 3 I could have multiplied by one third)

(obviously that example does not have the same ratio as your problem)

If the second ratio contained only two elements and I wanted to find the third then it can only be done if the two I have given are
in the correct ratio. If I chose 4 : 7 : ? then that would not be possible for 3 : 6 : 9 however if I change the 7 to an 8 then we get
4 : 8 : 12

In your example in the earlier post the problem is that the two numbers you gave for the new ratio are already incorrect relative
to each other. In other words one must be changed. Either the original measurements are wrong or the two numbers in the
second ratio are not in the right ratio relative to each other. The fact that the second number is larger than the first, but the other
way round in the other ratio immediately alerts a mathematician to an inconsistent proportion.

If I have the ratio 3 : 6 : 9 and I want a model to be 1 : 7 : ???  then the first number has to go from 3 to 1, but the second has
to go from 6 to 7, with the same multiplication. Well this is not going to work because 3 multiplied by a third equals 1
but if I do the same multiplication to the second number 6 get transformed to 2. One cannot go up and the other down.
In fact the two numbers that we give for the second ratio have to be in the correct ratio of the first two numbers of the first ratio.
It would probably by a good idea to look at Bob's post including the image file he posted (if you haven't already done so).
Trying to explain this using plain text only is not easy and could cause confusion.

Anyway I hope that has cleared the matter up rather than muddied the waters even further.

Whoa, I feel like your shooting my head.  Can you break it down with my original book example, I may get the math more easier ? smile

Last edited by SuperLynx (2013-04-19 17:41:54)

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#23 2013-11-12 14:55:39

SuperLynx
Member
Registered: 2009-06-28
Posts: 286

Re: Understanding Ratio to Scale ?

I need to re-open this subject as I feel Ill understand better. 

If I have an object that is 12 inches high, and 4 inches wide, and 24 inches deep, can this be converted to a scale ratio ? And if so, how can I be reversed back from a scale ratio to the imperial dimensions ?

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